Quantum fate of timelike naked singularity with scalar hair

TL;DR

This paper investigates the quantum behavior of a naked singularity with scalar hair, comparing particle-based and geometry-based quantization methods, and finds that geometry quantization resolves the singularity.

Contribution

It compares different quantum approaches to resolve a naked singularity, highlighting the importance of geometry quantization methods over particle-based ones.

Findings

Particles detect the singularity in fixed background methods.

Geometry quantization methods resolve the singularity.

Different quantization approaches yield conflicting results.

Abstract

We study the quantum fate of a naked curvature singularity sourced by a scalar field via several methods and compare the results obtained. The first method relies on relativistic quantum mechanics on a fixed background employing the Klein--Gordon and the Dirac equations for a static spacetime. We show that both the Klein--Gordon and the Dirac particles feel this singularity therefore this method does not provide its resolution. For comparison, we subsequently employ methods for quantizing the geometry itself. We selected the canonical quantization via conditional symmetries and as a last approach we use a maximal acceleration derivation in the covariant loop quantum gravity. In both of these approaches the singularity is resolved at the quantum level. We discuss these conflicting results bearing in mind that quantum particles probe classical geometry in the first approach while the last two methods quantize the geometry itself.